Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

• 作者: Fa-Kai Wen Xin Zhang
• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2021,（5）
• 所属期刊栏目: GENERAL
• 页码范围: 206-214
• 页数: 9页
• 语种: 英文
• DOI: 10.1088/1674-1056/abcf43

摘要

We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.